Summer school II: Summer school on singular Kählerian metrics and Hermitian geometry
Description
Daniele Angella: Cohomological properties and Hermitian metrics of complex non-Kähler manifolds
Tutor: Nicoletta Tardini
Abstract: the first lectures will provide a survey of the cohomological properties and topological aspects of complex manifolds, as well as canonical metrics on complex manifolds. We will then focus on some analytic problems concerning the geometry of the Chern connection on Hermitian manifolds, such as the existence of metrics with constant Chern-scalar curvature, generalizations of the Kähler-Einstein condition to the non-Kähler setting, the convergence of the Chern-Ricci flow on compact complex surfaces, and the asymptotic behavior of Monge-Ampère volumes of Hermitian metrics in the ddc-class.
Hans-Joachim Hein: Liouville theorems and Evans-Krylov estimates for the complex Monge-Ampère equation
Tutor: Yifan Chen
Abstract: A classical idea going back at least to work of Leon Simon (1997) is that Liouville theorems for solutions to elliptic or parabolic PDEs are equivalent to Schauder-type regularity estimates. The goal of this course is to describe some recent developments of this idea concerning the regularity of the complex Monge-Ampère equation with respect to singular reference metrics. We will start with a quick look at Yau's C^2 and C^3 estimates and then present a new proof of the Evans-Krylov C^{2,alpha} estimate on a Euclidean ball. Based on this we will consider the case of singular backgrounds such as cylinders and cones, discussing some parts of my recent joint work with V. Tosatti and M.-C. Lee and work of my former student J. Klemmensen.
REGISTRATION
The registration period has ended.
ACCOMMODATION
Limited financial support for accommodation is available for students and postdocs.
LOCAL EXPENSES
Apart from the above support in accommodation, we cannot cover local expenses.
IMPORTANT INFORMATION
The conference organizers do not authorize any external subjects to arrange or propose accommodation for the participants. If you receive e-mails from travel or housing agencies, etc., containing booking offers and requests for sending your personal data or advance payment, you should treat them as scams.
All official communications will only come from the Erdős Center secretary or directly from the organizers. Those who requested financial support for the accommodation will get the details directly from the secretary of the Erdős Center.
Venue: Main Lecture Hall, Rényi Institute
https://maps.app.goo.gl/RxdVNyhTAYXbzS2V8
The following link gives practical information (e.g. local traveling):
https://erdoscenter.renyi.hu/practicalities
Schedule
The schedule of the summer school and the schedule of the lightning talks and posters are available in Downloads below.
Conference Dinner
We invite all participants to the conference dinner on 14th August, Thursday at 7 pm at Stifler 32 Beerhouse on Rákóczi street 32 (a ten minute walk from the Institute)
You can walk there directly, or meet at 18:30 in the Rényi institute outside of the main lecture hall (same floor).